Expression of type And

from the theory of proveit.linear_algebra.linear_maps

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Function, K, P, Px, Py, V, W, c, x, y
from proveit.linear_algebra import ScalarMult, VecAdd
from proveit.logic import And, Equals, Forall, InSet

# build up the expression from sub-expressions
sub_expr1 = [x]
expr = And(Forall(instance_param_or_params = sub_expr1, instance_expr = InSet(Px, W), domain = V), Forall(instance_param_or_params = [x, y], instance_expr = Equals(Function(P, [VecAdd(x, y)]), VecAdd(Px, Py)), domain = V), Forall(instance_param_or_params = [c], instance_expr = Forall(instance_param_or_params = sub_expr1, instance_expr = Equals(Function(P, [ScalarMult(c, x)]), ScalarMult(c, Px)), domain = V), domain = K)).with_wrapping_at(2,4)

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\begin{array}{c} \left[\forall_{x \in V}~\left(P\left(x\right) \in W\right)\right] \land  \\ \left[\forall_{x, y \in V}~\left(P\left(x + y\right) = \left(P\left(x\right) + P\left(y\right)\right)\right)\right] \land  \\ \left[\forall_{c \in K}~\left[\forall_{x \in V}~\left(P\left(c \cdot x\right) = \left(c \cdot P\left(x\right)\right)\right)\right]\right] \end{array}

stored_expr.style_options()

name	description	default	current value	related methods
operation	'infix' or 'function' style formatting	infix	infix
wrap_positions	position(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.	()	(2 4)	('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	center	center	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Operation	operator: 22 operands: 1
1	ExprTuple	2, 3, 4
2	Operation	operator: 24 operand: 8
3	Operation	operator: 24 operand: 9
4	Operation	operator: 24 operand: 10
5	ExprTuple	8
6	ExprTuple	9
7	ExprTuple	10
8	Lambda	parameter: 61 body: 11
9	Lambda	parameters: 42 body: 12
10	Lambda	parameter: 60 body: 14
11	Conditional	value: 15 condition: 40
12	Conditional	value: 16 condition: 17
13	ExprTuple	60
14	Conditional	value: 18 condition: 19
15	Operation	operator: 46 operands: 20
16	Operation	operator: 44 operands: 21
17	Operation	operator: 22 operands: 23
18	Operation	operator: 24 operand: 31
19	Operation	operator: 46 operands: 26
20	ExprTuple	55, 27
21	ExprTuple	28, 29
22	Literal
23	ExprTuple	40, 30
24	Literal
25	ExprTuple	31
26	ExprTuple	60, 32
27	Variable
28	Operation	operator: 58 operand: 37
29	Operation	operator: 41 operands: 34
30	Operation	operator: 46 operands: 35
31	Lambda	parameter: 61 body: 36
32	Variable
33	ExprTuple	37
34	ExprTuple	55, 38
35	ExprTuple	48, 51
36	Conditional	value: 39 condition: 40
37	Operation	operator: 41 operands: 42
38	Operation	operator: 58 operand: 48
39	Operation	operator: 44 operands: 45
40	Operation	operator: 46 operands: 47
41	Literal
42	ExprTuple	61, 48
43	ExprTuple	48
44	Literal
45	ExprTuple	49, 50
46	Literal
47	ExprTuple	61, 51
48	Variable
49	Operation	operator: 58 operand: 54
50	Operation	operator: 56 operands: 53
51	Variable
52	ExprTuple	54
53	ExprTuple	60, 55
54	Operation	operator: 56 operands: 57
55	Operation	operator: 58 operand: 61
56	Literal
57	ExprTuple	60, 61
58	Variable
59	ExprTuple	61
60	Variable
61	Variable